The standard reaction Gibbs energy

Thermodynamic background

4.4 The standard reaction Gibbs energy

which an adjustment of the conformation of a molecule when one substrate binds affects the ease with which a subsequent substrate molecule binds. The details of the allosteric effect in hemoglobin will be explored in Case study10.4.

The differing shapes of the saturation curves for myoglobin and hemoglobin have important consequences for the way O₂is made available in the body: in particular, the greater sharpness of the Hb saturation curve means that Hb can load O₂more fully in the lungs and unload it more fully in different regions of the organism. In the lungs, where p

⬇

105 Torr (14 kPa), s

⬇

0.98, representing almost complete saturation. In resting muscular tissue, p is equivalent to about 38 Torr (5 kPa), corresponding to s

⬇

0.75, implying that sufficient O₂is still avail- able should a sudden surge of activity take place. If the local partial pressure falls to 22 Torr (3 kPa), s falls to about 0.1. Note that the steepest part of the curve falls in the range of typical tissue oxygen partial pressure. Myoglobin, on the other hand, begins to release O₂only when phas fallen below about 22 Torr, so it acts as a reserve to be drawn on only when the Hb oxygen has been used up. ■

Solution The standard reaction enthalpy is

rH^両 fH^両(H2CO3, aq){fH^両(CO2, g) fH^両(H2O, l)}

rH^両 699.65 kJ mol¹{(110.53 kJ mol¹)(285.83 kJ mol¹)}

rH^両 303.29 kJ mol¹

The standard reaction entropy was calculated in Illustration2.4:

rS^両 96.3 J K¹mol¹

which, because 96.3 J is the same as 9.63 10² kJ, corresponds to 9.63 10²kJ K¹mol¹. Therefore, from eqn 4.11,

rG^両(303.29 kJ mol¹)(298.15 K) (9.63 10²kJ K¹mol¹) rG^両 274.6 kJ mol¹

SELF-TEST 4.5 Use the information in the Data sectionto determine the stan- dard reaction Gibbs energy for 3 O2(g)ˆl2 O3(g) from standard enthalpies of formation and standard entropies.

Answer:326.4 kJ mol¹■

We saw in Section 1.14 how to use standard enthalpies of formation of sub- stances to calculate standard reaction enthalpies. We can use the same technique for standard reaction Gibbs energies. To do so, we list the standard Gibbs energy of formation,fG^両, of a substance, which is the standard reaction Gibbs energy (per mole of the species) for its formation from the elements in their reference states. The concept of reference state was introduced in Section 1.14; the temper- ature is arbitrary, but we shall almost always take it to be 25°C (298 K). For ex- ample, the standard Gibbs energy of formation of liquid water, fG^両(H₂O, l), is the standard reaction Gibbs energy for

H2(g)¹⁄2O2(g)ˆˆlH2O(l)

and is 237 kJ mol¹at 298 K. Some standard Gibbs energies of formation are listed in Table 4.2 and more can be found in the Data section. It follows from the definition that the standard Gibbs energy of formation of an element in its refer- ence state is zero because reactions such as

C(s, graphite)ˆˆlC(s, graphite)

are null (that is, nothing happens). The standard Gibbs energy of formation of an element in a phase different from its reference state is nonzero:

C(s, graphite)ˆˆlC(s, diamond) fG^両(C, diamond) 2.90 kJ mol¹ Many of the values in the tables have been compiled by combining the standard enthalpy of formation of the species with the standard entropies of the compound and the elements, as illustrated above, but there are other sources of data and we encounter some of them later.

Table 4.2

Standard Gibbs energies of formation at 298.15 K*

Substance ^fG^両/(kJ mol¹) Gases

Carbon dioxide, CO2 394.36

Methane, CH4 50.72

Nitrogen oxide, NO 86.55

Water, H2O 228.57

Liquids

Ethanol, CH3CH2OH 174.78 Hydrogen peroxide, H₂O₂ 120.35

Water, H2O 237.13

Solids

-D-Glucose C6H12O6 917.2 Glycine, CH₂(NH₂)COOH 532.9 Sucrose, C12H22O11 1543

Urea, CO(NH2)2 197.33

Solutes in aqueous solution

Carbon dioxide, CO₂ 385.98 Carbonic acid, H2CO3 623.08 Phosphoric acid, H3PO4 1018.7

*Additional values are given in the Data section.

Standard Gibbs energies of formation can be combined to obtain the standard Gibbs energy of almost any reaction. We use the now familiar expression

rG^両

冱

^{fG両(products)}

冱

^fG両(reactants) (4.12)

ILLUSTRATION 4.2 Calculating a standard reaction Gibbs energy from standard Gibbs energies of formation To determine the standard reaction Gibbs energy for the complete oxidation of solid sucrose, C₁₂H₂₂O₁₁(s), by oxygen gas to carbon dioxide gas and liquid water,

C₁₂H₂₂O₁₁(s)12 O₂(g)ˆˆl12 CO₂(g)11 H₂O(l) we carry out the following calculation:

rG^両{12fG^両(CO₂, g)11fG^両(H₂O, l)}

{fG^両(C₁₂H₂₂O₁₁, s)12fG^両(O₂, g)}

{12 (394 kJ mol¹)11 (237 kJ mol¹)}

{1543 kJ mol¹0}

5.79 10³kJ mol¹■

SELF-TEST 4.6 Calculate the standard reaction Gibbs energy of the oxidation of ammonia to nitric oxide according to the equation 4 NH₃(g)5 O₂(g)ˆl 4 NO(g)6 H₂O(g).

Answer:959.42 kJ mol¹

Standard Gibbs energies of formation of compounds have their own significance as well as being useful in calculations of K. They are a measure of the “thermody- namic altitude” of a compound above or below a “sea level” of stability represented by the elements in their reference states (Fig. 4.8). If the standard Gibbs energy of formation is positive and the compound lies above “sea level,” then the compound has a spontaneous tendency to sink toward thermodynamic sea level and decompose into the elements. That is, K1 for their formation reaction. We say that a com- pound with fG^両0 is thermodynamically unstablewith respect to its elements or that it is endergonic. Thus, the endergonic substance ozone, for which fG^両 163 kJ mol¹, has a spontaneous tendency to decompose into oxygen under stan- dard conditions at 25°C. More precisely, the equilibrium constant for the reaction

3⁄2O₂(g)ˆ0ˆ9O₃(g) is less than 1 (much less, in fact: K2.7 10²⁹). However, al- though ozone is thermodynamically unstable, it can survive if the reactions that con- vert it into oxygen are slow. That is the case in the upper atmosphere, and the O₃mol- ecules in the ozone layer survive for long periods. Benzene (fG^両 124 kJ mol¹) is also thermodynamically unstable with respect to its elements (K1.8 10²²).

However, the fact that bottles of benzene are everyday laboratory commodities also reminds us of the point made at the start of the chapter, that spontaneity is a thermo- dynamic tendency that might not be realized at a significant rate in practice.

Another useful point that can be made about standard Gibbs energies of forma- tion is that there is no point in searching for directsyntheses of a thermodynamically unstable compound from its elements (under standard conditions, at the temperature to which the data apply), because the reaction does not occur in the required direc- tion: the reversereaction, decomposition, is spontaneous. Endergonic compounds must be synthesized by alternative routes or under conditions for which their Gibbs energy of formation is negative and they lie beneath thermodynamic sea level.

Compounds with fG^両0 (corresponding to K1 for their formation reac- tions) are said to be thermodynamically stablewith respect to their elements or exergonic. Exergonic compounds lie below the thermodynamic sea level of the el- ements (under standard conditions). An example is the exergonic compound ethane, with fG^両 33 kJ mol¹: the negative sign shows that the formation of ethane gas is spontaneous in the sense that K1 (in fact, K7.1 10⁵at 25°C).